Introductory chemistry a foundation 7th edition 2

Writing Lewis Structures: Summary Give the Lewis structure for each of the following: Write the Lewis structures for the following molecules: You may wonder how to decide which atom is t

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Lewis Structures

To learn to write Lewis structures.

Bonding involves just the valence electrons of atoms Valence electrons are

trans-ferred when a metal and a nonmetal react to form an ionic compound Valence electrons are shared between nonmetals in covalent bonds

The Lewis structure is a representation of a molecule that shows how

the valence electrons are arranged among the atoms in the molecule Theserepresentations are named after G N Lewis, who conceived the idea whilelecturing to a class of general chemistry students in 1902 The rules for writ-ing Lewis structures are based on observations of many molecules from which

chemists have learned that the most important requirement for the formation of

a stable compound is that the atoms achieve noble gas electron configurations.

We have already seen this rule operate in the reaction of metals andnonmetals to form binary ionic compounds An example is the formation ofKBr, where the Kion has the [Ar] electron configuration and the Brion has

the [Kr] electron configuration In writing Lewis structures, we include only the valence electrons Using dots to represent valence electrons, we write the

Lewis structure for KBr as follows:

No dots are shown on the Kion because it has lost its only valence electron

(the 4s electron) The Brion is shown with eight electrons because it has afilled valence shell

Next we will consider Lewis structures for molecules with covalentbonds, involving nonmetals in the first and second periods The principle

of achieving a noble gas electron configuration applies to these elements asfollows:

1 Hydrogen forms stable molecules where it shares two electrons That

is, it follows a duet rule For example, when two hydrogen atoms,

each with one electron, combine to form the H2molecule, we have

By sharing electrons, each hydrogen in H2has, in effect, twoelectrons; that is, each hydrogen has a filled valence shell

2 Helium does not form bonds because its valence orbital is already

filled; it is a noble gas Helium has the electron configuration 1s2and can be represented by the Lewis structure

He[He] configuration

H H

K Noble gas configuration [Ar]

Noble gas configuration [Kr]

Br[ ]

370 Chapter 12 Chemical Bonding

12.6

O B J E C T I V E :

Remember that the electrons in

the highest principal energy

level of an atom are called the

valence electrons

G N Lewis in his lab.

Module 12: Drawing Lewis

Electron Dot Structures covers

concepts in this section.

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3 The second-row nonmetals carbon through fluorine form stablemolecules when they are surrounded by enough electrons to fill

the valence orbitals—that is, the one 2s and the three 2p orbitals.

Eight electrons are required to fill these orbitals, so these elements

typically obey the octet rule; they are surrounded by eight

electrons An example is the F2molecule, which has the followingLewis structure:

Note that each fluorine atom in F2is, in effect, surrounded by eightvalence electrons, two of which are shared with the other atom

This is a bonding pair of electrons, as we discussed earlier Each

fluorine atom also has three pairs of electrons that are not involved

in bonding These are called lone pairs or unshared pairs.

4 Neon does not form bonds because it already has an octet ofvalence electrons (it is a noble gas) The Lewis structure is

Note that only the valence electrons (2s22p6) of the neon atom

are represented by the Lewis structure The 1s2electrons are coreelectrons and are not shown

Next we want to develop some general procedures for writing Lewisstructures for molecules Remember that Lewis structures involve only thevalence electrons of atoms, so before we proceed, we will review the rela-tionship of an element’s position on the periodic table to the number of va-lence electrons it has Recall that the group number gives the total number

of valence electrons For example, all Group 6 elements have six valence

electrons (valence configuration ns2np4)

F ⎯⎯⎯⎯⎯⎯→ F F ←⎯⎯⎯⎯⎯⎯ F

12.6 Lewis Structures 371

Carbon, nitrogen, oxygen, and

fluorine almost always obey the

octet rule in stable molecules

Lewis structures show only

valence electrons

Group 6

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Similarly, all Group 7 elements have seven valence electrons (valence

con-figuration ns2np5)

Group 7

2 Atoms that are bonded to each other share one or more pairs ofelectrons

3 The electrons are arranged so that each atom is surrounded byenough electrons to fill the valence orbitals of that atom Thismeans two electrons for hydrogen and eight electrons for second-row nonmetals

The best way to make sure we arrive at the correct Lewis structure for amolecule is to use a systematic approach We will use the approach summa-rized by the following rules

Steps for Writing Lewis Structures

Step 1 Obtain the sum of the valence electrons from all of the atoms Do not

worry about keeping track of which electrons come from whichatoms It is the total number of valence electrons that is important

Step 2 Use one pair of electrons to form a bond between each pair of bound

atoms For convenience, a line (instead of a pair of dots) is often used

to indicate each pair of bonding electrons

Step 3 Arrange the remaining electrons to satisfy the duet rule for hydrogen

and the octet rule for each second-row element

To see how these rules are applied, we will write the Lewis structures ofseveral molecules

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scent Instead, they communicate the discovery of

a scent by body movements that the scientists call

“dances.” The device, called the Wasp Hound,contains a team of wasps in a hand-held venti-lated cartridge that has a fan at one end to draw

in air from outside If the scent is one the wasps

do not recognize, they continue flying randomly.However, if the scent is one the wasps have beenconditioned to recognize, they cluster around theopening A video camera paired with a computeranalyzes their behavior and signals when a scent

One of the problems we face in modern society

is how to detect illicit substances, such as drugs

and explosives, in a convenient, accurate

man-ner Trained dogs are often used for this purpose

because of their acute sense of smell Now

sev-eral researches are trying to determine whether

insects, such as honeybees and wasps, can be

even more effective chemical detectors In fact,

studies have shown that bees can be trained in

just a few minutes to detect the smell of almost

any chemical

Scientists at Los Alamos National Laboratory

in New Mexico are designing a portable device

using bees that possibly could be used to sniff out

drugs and bombs at airports, border crossings,

and schools They call their study the Stealthy

In-sect Sensor Project The Los Alamos project is

based on the idea that bees can be trained to

as-sociate the smell of a particular chemical with a

sugary treat Bees stick out their “tongues” when

they detect a food source By pairing a drop of

sugar water with the scent of TNT

(trinitro-toluene) or C-4 (composition 4) plastic explosive

about six times, the bees can be trained to extend

their proboscis at a whiff of the chemical alone

The bee bomb detector is about half the size of a

shoe box and weighs 4 lb Inside the box, bees are

lined up in a row and strapped into straw-like

tubes, then exposed to puffs of air as a camera

monitors their reactions The signals from the

video camera are sent to a computer, which

ana-lyzes the bees’ behavior and signals when the

bees respond to the particular scent they have

been trained to detect

A project at the University of Georgia uses

tiny parasitic wasps as a chemical detector Wasps

A honeybee receives a fragrant reminder of its target scent each morning and responds by sticking out its proboscis.

Writing Lewis Structures: Simple Molecules

Write the Lewis structure of the water molecule

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Step 1 Find the sum of the valence electrons for H2O.

(Group 1) (Group 1) (Group 6)

Step 2 Using a pair of electrons per bond, we draw in the two OOH bonds,using a line to indicate each pair of bonding electrons

HOOOHNote that

HOOOH represents

Step 3 We arrange the remaining electrons around the atoms to achieve anoble gas electron configuration for each atom Four electrons have beenused in forming the two bonds, so four electrons (8 4) remain to be dis-tributed Each hydrogen is satisfied with two electrons (duet rule), but oxy-gen needs eight electrons to have a noble gas electron configuration So theremaining four electrons are added to oxygen as two lone pairs Dots are used

to represent the lone pairs

This is the correct Lewis structure for the water molecule Each hydrogenshares two electrons, and the oxygen has four electrons and shares four togive a total of eight

Note that a line is used to represent a shared pair of electrons (bonding trons) and dots are used to represent unshared pairs

elec-Write the Lewis structure for HCl

See Problems 12.59 through 12.62 ■

Lewis Structures of Molecules with Multiple Bonds

To learn how to write Lewis structures for molecules with multiple bonds.

Now let’s write the Lewis structure for carbon dioxide

Step 1 Summing the valence electrons gives

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Step 2 Form a bond between the carbon and each oxygen:

OOCOO

Step 3 Next, distribute the remaining electrons to achieve noble gas tron configurations on each atom In this case twelve electrons (16 4) re-main after the bonds are drawn The distribution of these electrons is deter-mined by a trial-and-error process We have six pairs of electrons todistribute Suppose we try three pairs on each oxygen to give

elec-Is this correct? To answer this question we need to check two things:

already being undertaken by various oil panies Since 1996, the Norwegian oil companyStatoil has separated more than 1 million tons of

com-CO2 annually from natural gas and pumped itinto a saltwater aquifer beneath the floor of theNorth Sea In western Canada a group of oil com-panies has injected CO2from a North Dakota syn-thetic fuels plant into oil fields in an effort to in-crease oil recovery The oil companies expect tostore 22 million tons of CO2there and to produce

130 million barrels of oil over the next 20 years.Sequestration of CO2has great potential asone method for decreasing the rate of globalwarming Only time will tell whether it will work

As we discussed in Chapter 11 (see ”Chemistry

in Focus: Atmospheric Effects,” page 326), global

warming seems to be a reality At the heart of this

issue is the carbon dioxide produced by society’s

widespread use of fossil fuels For example, in the

United States, CO2makes up 81% of greenhouse

gas emissions Thirty percent of this CO2 comes

from coal-fired power plants used to produce

electricity One way to solve this problem would

be to phase out coal-fired power plants

How-ever, this outcome is not likely because the

United States possesses so much coal (at least a

250-year supply) and coal

is so cheap (about $0.03

per pound) Recognizing

this fact, the U.S

govern-ment has instituted a

re-search program to see

if the CO2 produced at

power plants can be

cap-tured and sequestered

(stored) underground in

deep geological

forma-tions The factors that

need to be explored to

determine whether

se-questration is feasible are

the capacities of

under-ground storage sites and

the chances that the sites

will leak

CO2 capture atpower stations

CO2 stored in geologic disposal

Enhanced oil recovery

Unmineable coal beds

Depleted oil

or gas reserves

Deep saline formation

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1 The total number of electrons There are sixteen valence electrons inthis structure, which is the correct number.

2 The octet rule for each atom Each oxygen has eight electronsaround it, but the carbon has only four This cannot be the correctLewis structure

How can we arrange the sixteen available electrons to achieve an octetfor each atom? Suppose we place two shared pairs between the carbon andeach oxygen:

Now each atom is surrounded by eight electrons, and the total number

of electrons is sixteen, as required This is the correct Lewis structure for

car-bon dioxide, which has two double car-bonds A single car-bond involves two

atoms sharing one electron pair A double bond involves two atoms

shar-ing two pairs of electrons

In considering the Lewis structure for CO2, you may have come up with

Note that both of these structures have the required sixteen electronsand that both have octets of electrons around each atom (verify this for

yourself) Both of these structures have a triple bond in which three

elec-tron pairs are shared Are these valid Lewis structures for CO2? Yes So therereally are three Lewis structures for CO2:

This brings us to a new term, resonance A molecule shows resonance when

more than one Lewis structure can be drawn for the molecule In such a case we

call the various Lewis structures resonance structures.

Of the three resonance structures for CO2shown above, the one in thecenter with two double bonds most closely fits our experimental informa-tion about the CO2molecule In this text we will not be concerned abouthow to choose which resonance structure for a molecule gives the “best” de-scription of that molecule’s properties

Next let’s consider the Lewis structure of the CN(cyanide) ion

Step 1 Summing the valence electrons, we have

Note that the negative charge means an extra electron must be added

Step 2 Draw a single bond (CON)

Step 3 Next, we distribute the remaining electrons to achieve a noble gasconfiguration for each atom Eight electrons remain to be distributed Wecan try various possibilities, such as

These structures are incorrect To show why none is a valid Lewis structure,count the electrons around the C and N atoms In the left structure, neither

8 electrons

O

represents

C OO

O

represents

C OO

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atom satisfies the octet rule In the center structure, C has eight electrons but

N has only four In the right structure, the opposite is true Remember thatboth atoms must simultaneously satisfy the octet rule Therefore, the correctarrangement is

(Satisfy yourself that both carbon and nitrogen have eight electrons.) In thiscase we have a triple bond between C and N, in which three electron pairsare shared Because this is an anion, we indicate the charge outside of squarebrackets around the Lewis structure

In summary, sometimes we need double or triple bonds to satisfy theoctet rule Writing Lewis structures is a trial-and-error process Start withsingle bonds between the bonded atoms and add multiple bonds asneeded

We will write the Lewis structure for NO2 in Example 12.3 to make surethe procedures for writing Lewis structures are clear

on the stomach walls and then reemerging aftertreatment ends

Studies at Johns Hopkins in Baltimore andVandoeuvre-les Nancy in France have shown that

sulforaphane kills H pylori (even when it has

taken refuge in stomach-wall cells) at tions that are achievable by eating broccoli Thescientists at Johns Hopkins also found that sul-foraphane seems to inhibit stomach cancer inmice Although there are no guarantees thatbroccoli will keep you healthy, it might not hurt

concentra-to add it concentra-to your diet

Eating the right foods is critical to our health In

particular, certain vegetables, although they do

not enjoy a very jazzy image, seem especially

im-portant A case in point is broccoli, a vegetable

with a humble reputation that packs a powerful

chemistry wallop

Broccoli contains a chemical called

sulfora-phane, which has the following Lewis structure:

Experiments indicate that sulforaphane furnishes

protection against certain cancers by increasing

the production of enzymes (called phase 2

en-zymes) that “mop up” reactive molecules that

can harm DNA Sulforaphane also seems to

bat bacteria For example, among the most

com-mon harmful bacteria in humans is Helicobacter

pylori (H pylori), which has been implicated in

the development of several diseases of the

stom-ach, including inflammation, cancer, and ulcers

Antibiotics are clearly the best treatment for H.

pylori infections However, especially in

develop-ing countries, where H pylori is rampant,

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Writing Lewis Structures: Resonance Structures

Write the Lewis structure for the NO2anion

S O L U T I O N Step 1 Sum the valence electrons for NO2

Valence electrons: 6 5 6 1 18 electrons

elec-Ozone is a very important constituent of the atmosphere At upper levels itprotects us by absorbing high-energy radiation from the sun Near the earth’ssurface it produces harmful air pollution Write the Lewis structure forozone, O3

See Problems 12.63 through 12.68 ■Now let’s consider a few more cases in Example 12.4

Writing Lewis Structures: Summary

Give the Lewis structure for each of the following:

Write the Lewis structures for the following molecules:

You may wonder how to decide

which atom is the central atom

in molecules of binary

com-pounds In cases where there is

one atom of a given element

and several atoms of a second

element, the single atom is

almost always the central atom

of the molecule

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Remember, when writing Lewis structures, you don’t have to worryabout which electrons come from which atoms in a molecule It is best tothink of a molecule as a new entity that uses all the available valence elec-trons from the various atoms to achieve the strongest possible bonds Think

of the valence electrons as belonging to the molecule, rather than to the dividual atoms Simply distribute all the valence electrons so that noble gaselectron configurations are obtained for each atom, without regard to theorigin of each particular electron

in-Some Exceptions to the Octet Rule

The idea that covalent bonding can be predicted by achieving noble gas tron configurations for all atoms is a simple and very successful idea Therules we have used for Lewis structures describe correctly the bonding in

elec-12.7 Lewis Structures of Molecules with Multiple Bonds 379

NO3showsresonance

H

F H

N N N

C H

H

C F

F

O

F

O N F

O O N

Draw Single Bonds

H

N

C H

H

C F

F F H

N N

O ] N [

O N

Use Remaining Electrons to Achieve Noble Gas Configurations

H F

H N

H C

F C

N O

N

Atom

2 8

8 8

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most molecules However, with such a simple model, some exceptions are evitable Boron, for example, tends to form compounds in which the boronatom has fewer than eight electrons around it—that is, it does not have acomplete octet Boron trifluoride, BF3, a gas at normal temperatures andpressures, reacts very energetically with molecules such as water and ammo-nia that have unshared electron pairs (lone pairs).

in-The violent reactivity of BF3with electron-rich molecules arises because theboron atom is electron-deficient The Lewis structure that seems most con-sistent with the properties of BF3(twenty-four valence electrons) is

Note that in this structure the boron atom has only six electrons around it.The octet rule for boron could be satisfied by drawing a structure with a dou-ble bond between the boron and one of the fluorines However, experimentsindicate that each BOF bond is a single bond in accordance with the aboveLewis structure This structure is also consistent with the reactivity of BF3with electron-rich molecules For example, BF3reacts vigorously with NH3toform H3NBF3

Note that in the product H3NBF3, which is very stable, boron has an octet ofelectrons

It is also characteristic of beryllium to form molecules where the lium atom is electron-deficient

beryl-The compounds containing the elements carbon, nitrogen, oxygen,and fluorine are accurately described by Lewis structures in the vast major-ity of cases However, there are a few exceptions One important example isthe oxygen molecule, O2 The following Lewis structure that satisfies theoctet rule can be drawn for O2(see Self-Check Exercise 12.4)

However, this structure does not agree with the observed behavior of oxygen.

For example, the photos in Figure 12.10 show that when liquid oxygen ispoured between the poles of a strong magnet, it “sticks” there until it boilsaway This provides clear evidence that oxygen is paramagnetic—that is, itcontains unpaired electrons However, the above Lewis structure shows onlypairs of electrons That is, no unpaired electrons are shown There is no sim-ple Lewis structure that satisfactorily explains the paramagnetism of the O2molecule

Any molecule that contains an odd number of electrons does not form to our rules for Lewis structures For example, NO and NO2have elevenand seventeen valence electrons, respectively, and conventional Lewis struc-tures cannot be drawn for these cases

con-Even though there are exceptions, most molecules can be described byLewis structures in which all the atoms have noble gas electron configura-tions, and this is a very useful model for chemists

OO

NHH

H

F

FF

→

FB

Paramagnetic substances have

unpaired electrons and are

drawn toward the space

between a magnet’s poles

Figure 12.10

When liquid oxygen is poured

between the poles of a magnet,

it “sticks” until it boils away

This shows that the O 2 molecule

has unpaired electrons (is

paramagnetic).

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Molecular Structure

To understand molecular structure and bond angles.

So far in this chapter we have considered the Lewis structures of molecules

These structures represent the arrangement of the valence electrons in a

ecule We use the word structure in another way when we talk about the

mol-ecular structure or geometric structure of a molecule These terms

re-fer to the three-dimensional arrangement of the atoms in a molecule For

example, the water molecule is known to have the molecular structure

which is often called “bent” or “V-shaped.” To describe the structure more

precisely, we often specify the bond angle For the H2O molecule the bondangle is about 105°

Computer graphic of a linear molecule

containing three atoms

On the other hand, some molecules exhibit a linear structure (all atoms

in a line) An example is the CO2molecule

Note that a linear molecule has a 180° bond angle

A third type of molecular structure is illustrated by BF3, which is planar

or flat (all four atoms in the same plane) with 120° bond angles

The name usually given to this structure is trigonal planar structure,

al-though triangular might seem to make more sense

Another type of molecular structure is illustrated by methane, CH4.This molecule has the molecular structure shown in Figure 12.11, which is

called a tetrahedral structure or a tetrahedron The dashed lines

shown connecting the H atoms define the four identical triangular faces ofthe tetrahedron

BF

The tetrahedral molecular

structure of methane This

representation is called a

ball-and-stick model; the atoms are

represented by balls and the

bonds by sticks The dashed

lines show the outline of the

tetrahedron.

H H

C H

H

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In the next section we will discuss these various molecular structures inmore detail In that section we will learn how to predict the molecular struc-ture of a molecule by looking at the molecule’s Lewis structure.

Molecular Structure: The VSEPR Model

To learn to predict molecular geometry from the number of electron pairs.

The structures of molecules play a very important role in determining theirproperties For example, as we see in the “Chemistry in Focus” on page 383,taste is directly related to molecular structure Structure is particularly im-portant for biological molecules; a slight change in the structure of a largebiomolecule can completely destroy its usefulness to a cell and may evenchange the cell from a normal one to a cancerous one

Many experimental methods now exist for determining the molecularstructure of a molecule—that is, the three-dimensional arrangement of theatoms These methods must be used when accurate information about the

structure is required However, it is often useful to be able to predict the proximate molecular structure of a molecule In this section we consider a

ap-simple model that allows us to do this This model, called the valence shell

electron pair repulsion (VSEPR) model, is useful for predicting the

molecular structures of molecules formed from nonmetals The main idea of

this model is that the structure around a given atom is determined by minimizing repulsions between electron pairs This means that the bonding and nonbonding electron pairs (lone pairs) around a given atom are positioned as far apart

as possible To see how this model works, we will first consider the molecule

BeCl2, which has the following Lewis structure (it is an exception to the octetrule):

Note that there are two pairs of electrons around the beryllium atom Whatarrangement of these electron pairs allows them to be as far apart as possible

to minimize the repulsions? The best arrangement places the pairs on site sides of the beryllium atom at 180° from each other

oppo-This is the maximum possible separation for two electron pairs Now that wehave determined the optimal arrangement of the electron pairs around thecentral atom, we can specify the molecular structure of BeCl2—that is, thepositions of the atoms Because each electron pair on beryllium is shared

with a chlorine atom, the molecule has a linear structure with a 180°

bond angle

Whenever two pairs of electrons are present around an atom, they should always

be placed at an angle of 180 to each other to give a linear arrangement.

Next let’s consider BF3, which has the following Lewis structure (it is other exception to the octet rule):

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Here the boron atom is surrounded by three pairs of electrons What ment minimizes the repulsions among three pairs of electrons? Here thegreatest distance between electron pairs is achieved by angles of 120°.

Taste—It’s the Structure That Counts

Why do certain substances taste sweet, sour,

bitter, or salty? Of course, it has to do with the

taste buds on our tongues But how do these

taste buds work? For example, why does sugar

taste sweet to us? The answer to this question

re-mains elusive, but it does seem clear that sweet

taste depends on how certain molecules fit the

“sweet receptors” in our taste buds

One of the mysteries of the sweet taste

sen-sation is the wide variety of molecules that taste

sweet For example, the many types of sugars

in-clude glucose and sucrose (table sugar) The first

artificial sweetener was probably the Romans’

sapa (see “Chemistry in Focus: Sugar of Lead” in

Chapter 5), made by boiling wine in lead vessels to

produce a syrup that contained lead acetate,

Pb(C2H3O2)2, called sugar of lead because of its

sweet taste Other widely used modern artificial

sweeteners include saccharin, aspartame,

sucra-lose, and steviol, whose structures are shown in

the accompanying figure The structure of

steviol is shown in simplified form Each

ver-tex represents a carbon atom, and not all of

the hydrogen atoms are shown Note the

great disparity of structures for these

sweet-tasting molecules It’s certainly not obvious

which structural features trigger a sweet

sen-sation when these molecules interact with

the taste buds

The pioneers in relating structure to

sweet taste were two chemists, Robert S

Shallenberger and Terry E Acree of Cornell

University, who almost thirty years ago

sug-gested that all sweet-tasting substances must

contain a common feature they called a

gly-cophore They postulated that a glycophore

always contains an atom or group of atoms

that have available electrons located near a

hydrogen atom attached to a relatively

elec-tronegative atom Murray Goodman, a chemist atthe University of California at San Diego, ex-panded the definition of a glycophore to include ahydrophobic (“water-hating”) region Goodmanfinds that a “sweet molecule” tends to be L-shaped with positively and negatively charged re-gions on the upright of the L and a hydrophobicregion on the base of the L For a molecule to besweet, the L must be planar If the L is twisted inone direction, the molecule has a bitter taste Ifthe molecule is twisted in the other direction, themolecule is tasteless

The latest model for the sweet-taste tor, proposed by Piero Temussi of the University

recep-of Naples, postulates that there are four bindingsites on the receptor that can be occupied inde-pendently Small sweet-tasting molecules mightbind to one of the sites, while a large moleculewould bind to more than one site simultaneously

So the search goes on for a better artificialsweetener One thing’s for sure; it all has to dowith molecular structure

Aspartame (Nutra-Sweet™)

OH

O

CH 2 C O

N H

N

H

H H H

O

H H

H

C C

C C C C

C NH C C C

O

C S

H

H H

H H H

H H

H OH

Cl

C O

H H H H HO HO

Steviol

O

OH

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Because each of the electron pairs is shared with a fluorine atom, the ular structure is

mo-lec-This is a planar (flat) molecule with a triangular arrangement of F atoms,

commonly described as a trigonal planar structure Whenever three pairs of electrons are present around an atom, they should always be placed at the corners

of a triangle (in a plane at angles of 120° to each other).

Next let’s consider the methane molecule, which has the Lewis structure

There are four pairs of electrons around the central carbon atom Whatarrangement of these electron pairs best minimizes the repulsions? First wetry a square planar arrangement:

The carbon atom and the electron pairs are all in a plane represented by thesurface of the paper, and the angles between the pairs are all 90°

Is there another arrangement with angles greater than 90° that wouldput the electron pairs even farther away from each other? The answer is yes

We can get larger angles than 90° by using the following three-dimensionalstructure, which has angles of approximately 109.5°

In this drawing the wedge indicates a position above the surface of the per and the dashed lines indicate positions behind that surface The solidline indicates a position on the surface of the page The figure formed byconnecting the lines is called a tetrahedron, so we call this arrangement of

pa-electron pairs the tetrahedral arrangement.

This is the maximum possible separation of four pairs around a given atom

Whenever four pairs of electrons are present around an atom, they should always

be placed at the corners of a tetrahedron (the tetrahedral arrangement).

Now that we have the arrangement of electron pairs that gives the leastrepulsion, we can determine the positions of the atoms and thus the mo-lecular structure of CH In methane each of the four electron pairs is shared

120

A tetrahedron has four

equal triangular faces.

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between the carbon atom and a hydrogen atom Thus the hydrogen atomsare placed as shown in Figure 12.12, and the molecule has a tetrahedralstructure with the carbon atom at the center.

Recall that the main idea of the VSEPR model is to find the ment of electron pairs around the central atom that minimizes the repul-

arrange-sions Then we can determine the molecular structure by knowing how the

electron pairs are shared with the peripheral atoms A systematic procedurefor using the VSEPR model to predict the structure of a molecule is outlinedbelow

12.9 Molecular Structure: The VSEPR Model 385

Figure 12.12

The molecular structure of

methane The tetrahedral

arrangement of electron pairs

produces a tetrahedral

arrange-ment of hydrogen atoms.

H H

C H

H

Steps for Predicting Molecular Structure Using the VSEPR Model

Step 1 Draw the Lewis structure for the molecule.

Step 2 Count the electron pairs and arrange them in the way that minimizes

repulsion (that is, put the pairs as far apart as possible)

Step 3 Determine the positions of the atoms from the way the electron pairs

are shared

Step 4 Determine the name of the molecular structure from the positions of

the atoms

Predicting Molecular Structure Using the VSEPR Model, I

Ammonia, NH3, is used as a fertilizer (injected into the soil) and as a hold cleaner (in aqueous solution) Predict the structure of ammonia usingthe VSEPR model

house-S O L U T I O N Step 1 Draw the Lewis structure

Step 2 Count the pairs of electrons and arrange them to minimize sions The NH3molecule has four pairs of electrons around the N atom: threebonding pairs and one nonbonding pair From the discussion of the meth-ane molecule, we know that the best arrangement of four electron pairs isthe tetrahedral structure shown in Figure 12.13a

repul-Step 3 Determine the positions of the atoms The three H atoms shareelectron pairs as shown in Figure 12.13b

Step 4 Name the molecular structure It is very important to recognize that

the name of the molecular structure is always based on the positions of the atoms The placement of the electron pairs determines the structure, but the name

is based on the positions of the atoms Thus it is incorrect to say that the NH3

molecule is tetrahedral It has a tetrahedral arrangement of electron pairs but

not a tetrahedral arrangement of atoms The molecular structure of

ammo-nia is a trigonal pyramid (one side is different from the other three) rather

than a tetrahedron ■

HH

EXAMPLE 12.5

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Predicting Molecular Structure Using the VSEPR Model, II

Describe the molecular structure of the water molecule

S O L U T I O N Step 1 The Lewis structure for water is

Step 2 There are four pairs of electrons: two bonding pairs and two bonding pairs To minimize repulsions, these are best arranged in a tetrahe-dral structure as shown in Figure 12.14a

H

Lone pair

Bonding pair

N

The tetrahedral rangement of electron pairs around the nitrogen atom in the ammonia molecule.

ar-b

Three of the electron pairs around nitrogen are shared with hydrogen atoms as shown, and one is a lone pair Although the arrangement of electron pairs is tetrahedral, as in the methane molecule, the hydrogen atoms in the ammonia molecule occupy only three corners of the tetrahedron A lone pair occupies the fourth corner.

The NH 3 molecule has the trigonal pyramid structure (a pyramid with

ar-b

Two of the electron pairs are shared between oxygen and the hydrogen atoms, and two are lone pairs.

c

The V-shaped molecular structure of the water molecule.

Lone pair

Bonding pair

Trang 18

Step 3 Although H2O has a tetrahedral arrangement of electron pairs, it is not a tetrahedral molecule The atoms in the H2O molecule form a V shape, asshown in Figure 12.14b and c.

Step 4 The molecular structure is called V-shaped or bent

Predict the arrangement of electron pairs around the central atom Thensketch and name the molecular structure for each of the following molecules

on the following page Note the following general rules

12.10 Molecular Structure: Molecules with Double Bonds 387

Self-Check EXERCISE 12.5

Rules for Predicting Molecular Structure Using the VSEPR Model

1 Two pairs of electrons on a central atom in a molecule are always placed180° apart This is a linear arrangement of pairs

2 Three pairs of electrons on a central atom in a molecule are always placed120° apart in the same plane as the central atom This is a trigonal planar(triangular) arrangement of pairs

3 Four pairs of electrons on a central atom in a molecule are always placed109.5° apart This is a tetrahedral arrangement of electron pairs

4 When every pair of electrons on the central atom is shared with anotheratom, the molecular structure has the same name as the arrangement ofelectron pairs

Number of Pairs Name of Arrangement

Molecular Structure: Molecules with Double Bonds

To learn to apply the VSEPR model to molecules with double bonds.

Up to this point we have applied the VSEPR model only to molecules (andions) that contain single bonds In this section we will show that this modelapplies equally well to species with one or more double bonds We will de-velop the procedures for dealing with molecules with double bonds by con-sidering examples whose structures are known

O B J E C T I V E :

12.10

Trang 19

First we will examine the structure of carbon dioxide, a substance thatmay be contributing to the warming of the earth The carbon dioxide mole-cule has the Lewis structure

as discussed in Section 12.7 Carbon dioxide is known by experiment to be alinear molecule That is, it has a 180° bond angle

Recall from Section 12.9 that two electron pairs around a central atomcan minimize their mutual repulsions by taking positions on opposite sides

of the atom (at 180° from each other) This causes a molecule like BeCl2,which has the Lewis structure

to have a linear structure Now recall that CO2has two double bonds and isknown to be linear, so the double bonds must be at 180° from each other

Therefore, we conclude that each double bond in this molecule acts tively as one repulsive unit This conclusion makes sense if we think of a

effec-bond in terms of an electron density “cloud” between two atoms For ple, we can picture the single bonds in BeCl2as follows:

Table 12.4 Arrangements of Electron Pairs and the Resulting Molecular Structures for Two, Three, and Four Electron Pairs

Number of Electron Pair Ball-and-Stick Molecular Partial Lewis Ball-and-Stick

B F

B A

120˚

Cl Be Cl 180˚

A B A

109.5˚

H NHHA

B A

A

109.5˚

C H H H H A

B A

A A

109.5˚

Trang 20

The minimum repulsion between these two electron density clouds occurswhen they are on opposite sides of the Be atom (180° angle between them).Each double bond in CO2 involves the sharing of four electrons be-tween the carbon atom and an oxygen atom Thus we might expect thebonding cloud to be “fatter” than for a single bond:

However, the repulsive effects of these two clouds produce the same result asfor single bonds; the bonding clouds have minimum repulsions when theyare positioned on opposite sides of the carbon The bond angle is 180°, and

so the molecule is linear:

In summary, examination of CO2leads us to the conclusion that in ing the VSEPR model for molecules with double bonds, each double bondshould be treated the same as a single bond In other words, although a dou-ble bond involves four electrons, these electrons are restricted to the space

389

its bonds are sensitive to specific wavelengths oflight When azobenzene absorbs light of 420 nm,

it becomes extended; light at 365 nm causes themolecule to contract

To make their tiny machine, the German entists attached one end of the azobenzenepolymer to a tiny, bendable lever similar to thetip of an atomic-force microscope The other end

sci-of the polymer was attached to a glass surface.Flashes of 365-nm light caused the molecule tocontract, bending the lever down and storingmechanical energy Pulses of 420-nm radiationthen extended the molecule, causing the lever torise and releasing the stored energy Eventually,one can imagine having the lever operate somepart of a nanoscale machine It seems we are get-ting close to the ultimate in miniature machines

Our modern society is characterized by a

con-tinual quest for miniaturization Our computers,

cell phones, portable music players, calculators,

and many other devices have been greatly

down-sized over the last several years The ultimate in

miniaturization—machines made of single

mole-cules Although this idea sounds like an

impossi-ble dream, recent advances place us on the

doorstep of such devices For example, Hermann

E Gaub and his coworkers at the Center for

Nanoscience at Ludwig-Maximilians University in

Munich have just reported a single molecule that

can do simple work

Gaub and his associates constructed a

poly-mer about 75 nm long by hooking together

many light-sensitive molecules called

azoben-zenes:

CN

HC

CH

Trang 21

between a given pair of atoms Therefore, these four electrons do not tion as two independent pairs but are “tied together” to form one effectiverepulsive unit.

func-We reach this same conclusion by considering the known structures ofother molecules that contain double bonds For example, consider the ozonemolecule, which has eighteen valence electrons and exhibits two resonancestructures:

The ozone molecule is known to have a bond angle close to 120° Recall that120° angles represent the minimum repulsion for three pairs of electrons

This indicates that the double bond in the ozone molecule is behaving asone effective repulsive unit:

These and other examples lead us to the following rule: When using the VSEPR model to predict the molecular geometry of a molecule, a double bond is counted the same as a single electron pair.

Thus CO2 has two “effective pairs” that lead to its linear structure,whereas O3has three “effective pairs” that lead to its bent structure with a120° bond angle Therefore, to use the VSEPR model for molecules (or ions)that have double bonds, we use the same steps as those given in Section 12.9,but we count any double bond the same as a single electron pair Although

we have not shown it here, triple bonds also count as one repulsive unit inapplying the VSEPR model

Predicting Molecular Structure Using the VSEPR Model, III

Predict the structure of the nitrate ion

S O L U T I O N Step 1 The Lewis structures for NO3are

Step 2 In each resonance structure there are effectively three pairs of trons: the two single bonds and the double bond (which counts as one pair)

elec-O

NO

↔

O

NO

↔

O

NO

Trang 22

Step 4 The NO3 ion has a trigonal planar structure ■

directs you to the Chemistry in Focusfeature in the chapter indicates visual problems

interactive versions of these problems are assignable in OWL

tetrahedral arrangement (12.9) trigonal pyramid (12.9)

Key Terms

Summary

1 Chemical bonds hold groups of atoms together They

can be classified into several types An ionic bond is

formed when a transfer of electrons occurs to form

ions; in a purely covalent bond, electrons are shared

equally between identical atoms Between these

ex-tremes lies the polar covalent bond, in which

elec-trons are shared unequally between atoms with

dif-ferent electronegativities.

2 Electronegativity is defined as the relative ability of

an atom in a molecule to attract the electrons shared

in a bond The difference in electronegativity values

between the atoms involved in a bond determines

the polarity of that bond.

3 In stable chemical compounds, the atoms tend to

achieve a noble gas electron configuration In the

for-mation of a binary ionic compound involving

repre-sentative elements, the valence-electron

configura-tion of the nonmetal is completed: it achieves the

configuration of the next noble gas The valence

or-bitals of the metal are emptied to give the electron configuration of the previous noble gas Two nonmetals share the valence electrons so that both atoms have completed valence-electron configurations (noble gas configurations).

4 Lewis structures are drawn to represent the

arrange-ment of the valence electrons in a molecule The rules for drawing Lewis structures are based on the obser- vation that nonmetal atoms tend to achieve noble gas electron configurations by sharing electrons This leads to a duet rule for hydrogen and to an octet rule for many other atoms.

5 Some molecules have more than one valid Lewis

struc-ture, a property called resonance Although Lewis structures in which the atoms have noble gas electron configurations correctly describe most molecules, there are some notable exceptions, including O2, NO,

NO2, and the molecules that contain Be and B.

6 The molecular structure of a molecule describes how

the atoms are arranged in space.

7 The molecular structure of a molecule can be

pre-dicted by using the valence shell electron pair sion (VSEPR) model This model bases its prediction

repul-on minimizing the repulsirepul-ons amrepul-ong the electrrepul-on pairs around an atom, which means arranging the electron pairs as far apart as possible.

Active Learning Questions

These questions are designed to be considered by groups of students in class Often these questions work well for in- troducing a particular topic in class.

1 Using only the periodic table, predict the most stable

ion for Na, Mg, Al, S, Cl, K, Ca, and Ga Arrange these elements from largest to smallest radius and explain why the radius varies as it does.

Trang 23

2 Write the proper charges so that an alkali metal, a

no-ble gas, and a halogen have the same electron

con-figurations What is the number of protons in each?

The number of electrons in each? Arrange them from

smallest to largest radii and explain your ordering

ra-tionale.

3 What is meant by a chemical bond?

4 Why do atoms form bonds with one another? What

can make a molecule favored compared with the lone

atoms?

5 How does a bond between Na and Cl differ from a

bond between C and O? What about a bond between

N and N?

6 In your own words, what is meant by the term

elec-tronegativity? What are the trends across and down the

periodic table for electronegativity? Explain them,

and describe how they are consistent with trends of

ionization energy and atomic radii.

7 Explain the difference between ionic bonding and

covalent bonding How can we use the periodic table

to help us determine the type of bonding between

atoms?

8 True or false? In general, a larger atom has a smaller

electronegativity Explain.

9 Why is there an octet rule (and what does octet mean)

in writing Lewis structures?

10 Does a Lewis structure tell which electrons came from

which atoms? Explain.

11 If lithium and fluorine react, which has more

attrac-tion for an electron? Why?

12 In a bond between fluorine and iodine, which has

more attraction for an electron? Why?

13 We use differences in electronegativity to account for

certain properties of bond.

What if all atoms had the same electronegativity

val-ues? How would bonding between atoms be affected?

What are some differences we would notice?

14 Explain how you can use the periodic table to predict

the formula of compounds.

15 Why do we only consider the valence electrons in

drawing Lewis structures?

16 How do we determine the total number of valence

electrons for an ion? Provide an example of an anion

and a cation, and explain your answer.

17 What is the main idea in the valence shell electron

pair repulsion (VSEPR) theory?

18 The molecules NH3and BF3 have the same general

formula (AB3) but different shapes.

a Find the shape of each of the above molecules.

b Provide more examples of real molecules that have

the same general formulas but different shapes.

19 How do we deal with multiple bonds in VSEPR theory?

20 In Section 12.10 of your text, the term “effective

pairs” is used What does this mean?

21 Consider the ions Sc3+ , Cl - , K + , Ca 2+ , and S 2- Match these ions to the following pictures that represent the relative sizes of the ions.

22 Write the name of each of the following shapes of

molecules.

Questions and Problems

12.1 Types of Chemical Bonds

Q U E S T I O N S

1 In general terms, what is a chemical bond?

2 What does the bond energy of a chemical bond

repre-sent?

3 A What sorts of elements react to form ionic

com-pounds?

4 In general terms, what is a covalent bond?

5 Describe the type of bonding that exists in the Cl2( g)

molecule How does this type of bonding differ from

that found in the HCl( g) molecule? How is it similar?

6 Compare and contrast the bonding found in the

H2( g) and HF( g) molecules with that found in NaF(s).

12.2 Electronegativity

7 The relative ability of an atom in a molecule to attract

electrons to itself is called the atom’s

8 What does it mean to say that a bond is polar? Give

two examples of molecules with polar bonds Indicate

in your examples the direction of the polarity.

9 A bond between atoms having a (small/large)

differ-ence in electronegativity will be ionic.

10 What factor determines the relative level of polarity

of a polar covalent bond?

c b

a

All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide

VP

Trang 24

P R O B L E M S

11 In each of the following groups, which element is

the most electronegative? Which is the least

electro-negative?

a K, Na, H

b F, Br, Na

c B, N, F

12 In each of the following groups, which element is

the most electronegative? Which is the least

electro-negative?

a Rb, Sr, I

b Ca, Mg, Sr

c Br, Ca, K

13 On the basis of the electronegativity values given in

Figure 12.3, indicate whether each of the following

bonds would be expected to be ionic, covalent, or

po-lar covalent.

a OOO

b AlOO

c BOO

bonds would be expected to be covalent, polar

Figure 12.3, indicate which is the more polar bond in

each of the following pairs.

a HOF or HOCl

b HOCl or HOI

c HOBr or HOCl

d HOI or HOBr

a OOCl or OOBr c POS or POO

b NOO or NOF d HOO or HON

19 Which bond in each of the following pairs has the

greater ionic character?

a NaOF or NaOI c LiOCl or CsOCl

b CaOS or CaOO d MgON or MgOP

20 Which bond in each of the following pairs has less

ionic character?

a NaOCl or CaOCl c FeOI or FeOF

b CsOCl or BaOCl d BeOF or BaOF

12.3 Bond Polarity and Dipole Moments

21 What is a dipole moment? Give four examples of

mol-ecules that possess dipole moments, and draw the rection of the dipole as shown in Section 12.3.

di-22 Why is the presence of a dipole moment in the water

molecule so important? What are some properties of water that are determined by its polarity?

P R O B L E M S

23 In each of the following diatomic molecules, which

end of the molecule is negative relative to the other end?

a hydrogen chloride, HCl

b carbon monoxide, CO

c bromine monofluoride, BrF

24 In each of the following diatomic molecules, which

end of the molecule is positive relative to the other end?

a hydrogen fluoride, HF

b chlorine monofluoride, ClF

c iodine monochloride, ICl

25 For each of the following bonds, draw a figure

indicat-ing the direction of the bond dipole, includindicat-ing which end of the bond is positive and which is negative.

a COF c COO

b SiOC d BOC

a SOO c SOF

b SON d SOCl

a SiOH c SOH

b POH d ClOH

Trang 25

12.4 Stable Electron Configurations

and Charges on Ions

29 What does it mean when we say that in forming

bonds, atoms try to achieve an electron

configura-tion analogous to a noble gas?

30 The metallic elements lose electrons when reacting,

and the resulting positive ions have an electron

con-figuration analogous to the noble gas

element.

31 Nonmetals form negative ions by (losing/gaining)

enough electrons to achieve the electron

configura-tion of the next noble gas.

32 Explain how the atoms in covalent molecules achieve

electron configurations similar to those of the noble

gases How does this differ from the situation in ionic

compounds?

P R O B L E M S

33 Which simple ion would each of the following

ele-ments be expected to form? What noble gas has an

analogous electron configuration to each of the ions?

a chlorine, Z 17

b strontium, Z 38

c oxygen, Z 8

d rubidium, Z 37

34 Which simple ion would each of the following

ele-ments be expected to form? Which noble gas has an

analogous electron configuration to each of the ions?

a bromine, Z 35

b cesium, Z 55

c phosphorus, Z 15

d sulfur, Z 16

35 For each of the following numbers of electrons, give

the formula of a positive ion that would have that

number of electrons, and write the complete electron

configuration for each ion.

a 10 electrons c 18 electrons

b 2 electrons d 36 electrons

36 Give the formula of a negative ion that would have

the same number of electrons as each of the

follow-ing positive ions.

a Na c Al3

b Ca2 d Rb

37 On the basis of their electron configurations, predict

the formula of the simple binary ionic compounds

likely to form when the following pairs of elements

react with each other.

a aluminum, Al, and sulfur, S

b radium, Ra, and oxygen, O

c calcium, Ca, and fluorine, F

d cesium, Cs, and nitrogen, N

e rubidium, Rb, and phosphorus, P

the formula of the simple binary ionic compound likely to form when the following pairs of elements react with each other.

a aluminum and bromine

b aluminum and oxygen

c aluminum and phosphorus

d aluminum and hydrogen

39 Name the noble gas atom that has the same electron

configuration as each of the ions in the following compounds.

a barium sulfide, BaS

b strontium fluoride, SrF2

c magnesium oxide, MgO

d aluminum sulfide, Al2S3

40 Atoms form ions so as to achieve electron

configura-tions similar to those of the noble gases For the lowing pairs of noble gas configurations, give the formulas of two simple ionic compounds that would have comparable electron configurations.

fol-a [He] and [Ne] c [He] and [Ar]

b [Ne] and [Ne] d [Ne] and [Ar]

12.5 Ionic Bonding and Structures

of Ionic Compounds

41 Is the formula we write for an ionic compound the

molecular formula or the empirical formula? Why?

42 Describe in general terms the structure of ionic solids

such as NaCl How are the ions packed in the crystal?

43 Why are cations always smaller than the atoms from

which they are formed?

44 Why are anions always larger than the atoms from

which they are formed?

P R O B L E M S

45 For each of the following pairs, indicate which

species is smaller Explain your reasoning in terms of the electron structure of each species.

a H or H c Al or Al3

b N or N3 d F or Cl

46 For each of the following pairs, indicate which

species is larger Explain your reasoning in terms of the electron structure of each species.

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12.6 and 12.7 Lewis Structures

49 Why are the valence electrons of an atom the only

electrons likely to be involved in bonding to other

atoms?

50 Explain what the “duet” and “octet” rules are and

how they are used to describe the arrangement of

electrons in a molecule.

51 What type of structure must each atom in a

com-pound usually exhibit for the comcom-pound to be stable?

52 When elements in the second and third periods occur

in compounds, what number of electrons in the

va-lence shell represents the most stable electron

arrangement? Why?

P R O B L E M S

53 How many electrons are involved when two atoms in

a molecule are connected by a “double bond”? Write

the Lewis structure of a molecule containing a double

bond.

54 What does it mean when two atoms in a molecule are

connected by a “triple bond”? Write the Lewis

struc-ture of a molecule containing a triple bond.

55 Write the simple Lewis structure for each of the

57 Give the total number of valence electrons in each of

the following molecules.

a N2O c C3H8

b B2H6 d NCl3

58 Give the total number of valence electrons in each of

the following molecules.

a B2O3 c C2H6O

b CO2 d NO2

59 Write a Lewis structure for each of the following

sim-ple molecules Show all bonding valence electron

pairs as lines and all nonbonding valence electron

pairs as dots.

a NBr3 c CBr4

b HF d C2H2

sim-ple molecules Show all bonding valence electron

pairs as lines and all nonbonding valence electron

pairs as dots.

a H2 c CF4

b Hcl d C2F6

sim-ple molecules Show all bonding valence electron pairs as lines and all nonbonding valence electron pairs as dots.

a C2H6 c C4H10

b NF3 d SiCl4

mol-ecules Show all bonding valence electron pairs as lines and all nonbonding valence electron pairs as dots.

a PCl3 c C2H4Cl2

b CHCl3 d N2H4

63 The “Chemistry in Focus” segment Broccoli–Miracle

Food? discusses the health benefits of eating broccoli

and gives a Lewis structure for sulforaphane, a ical in broccoli Draw possible resonance structures for sulforaphane.

chem-64 The “Chemistry in Focus” segment Hiding Carbon

Dioxide discusses attempts at sequestering (storing)

underground CO2produced at power plants so as to diminish the greenhouse effect Draw all resonance structures of the CO2molecule.

poly-atomic ions Show all bonding valence electron pairs

as lines and all nonbonding valence electron pairs as dots For those ions that exhibit resonance, draw the various possible resonance forms.

a sulfate ion, SO4

b phosphate ion, PO4

c sulfite ion, SO3

a chlorate ion, ClO3

b peroxide ion, O2

c acetate ion, C2H3O2

a chlorite ion, ClO2

b perbromate ion, BrO4

c cyanide ion, CN

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12.8 Molecular Structure

69 What is the geometric structure of the water

mole-cule? How many pairs of valence electrons are there

on the oxygen atom in the water molecule? What is

the approximate HOOOH bond angle in water?

70 What is the geometric structure of the ammonia

mol-ecule? How many pairs of electrons surround the

ni-trogen atom in NH3? What is the approximate

HONOH bond angle in ammonia?

71 What is the geometric structure of the boron

trifluo-ride molecule, BF3? How many pairs of valence

elec-trons are present on the boron atom in BF3? What are

the approximate FOBOF bond angles in BF 3 ?

72 What is the geometric structure of the SiF4molecule?

How many pairs of valence electrons are present on

the silicon atom of SiF4? What are the approximate

FOSiOF bond angles in SiF 4 ?

12.9 Molecular Structure: The VSEPR Model

73 Why is the geometric structure of a molecule

impor-tant, especially for biological molecules?

74 What general principles determine the molecular

structure (shape) of a molecule?

75 How is the structure around a given atom related to

re-pulsion between valence electron pairs on the atom?

76 Why are all diatomic molecules linear, regardless of

the number of valence electron pairs on the atoms

involved?

77 Although the valence electron pairs in ammonia

have a tetrahedral arrangement, the overall

geomet-ric structure of the ammonia molecule is not

de-scribed as being tetrahedral Explain.

78 Although both the BF3 and NF3 molecules contain

the same number of atoms, the BF3molecule is flat,

whereas the NF3 molecule is trigonal pyramidal

Explain.

P R O B L E M S

79 For the indicated atom in each of the following

mol-ecules or ions, give the number and arrangement of

the electron pairs around that atom.

a As in AsO4

b Se in SeO4

c S in H2S

mol-ecules or ions, give the number and arrangement of

the electron pairs around that atom.

a S in SO3

b S in HSO3

c S in HS

81 Using the VSEPR theory, predict the molecular

struc-ture of each of the following molecules.

a NCl3 b H2Se c SiCl4

a NI3 b AsH3 c OF2

struc-ture of each of the following polyatomic ions.

a sulfate ion, SO4

b phosphate ion, PO4

c ammonium ion, NH4

a dihydrogen phosphate ion, H2PO4

b perchlorate ion, ClO4

c sulfite ion, SO3

85 For each of the following molecules or ions, indicate

the bond angle expected between the central atom and any two adjacent hydrogen atoms.

a H2O b NH3 c NH4 d CH4

86 For each of the following molecules or ions, indicate

the bond angle expected between the central atom and any two adjacent chlorine atoms.

a Cl2O b NCl3 c CCl4 d C2Cl4

87 The “Chemistry in Focus” segment Taste–It’s the

Struc-ture That Counts discusses artificial sweeteners What

are the expected bond angles around the nitrogen atom in aspartame?

88 The “Chemistry in Focus” segment Minimotor

Mole-cule discusses a tiny polymer (75 nm long) made of

azobenzenes that can do work Consider the Lewis structure shown in this segment What are the expected bond angles around the carbon atoms in the structure? What about the CONON bond angle?

Additional Problems

89 What is resonance? Give three examples of molecules

or ions that exhibit resonance, and draw Lewis tures for each of the possible resonance forms.

struc-90 When two atoms share two pairs of electrons, a(n)

bond is said to exist between them.

91 The geometric arrangement of electron pairs around a

given atom is determined principally by the tendency

to minimize between the electron pairs.

92 In each case, which of the following pairs of bonded

elements forms the more polar bond?

a SOF or SOCl

b NOO or POO

c COH or SiOH

F

Trang 28

93 In each case, which of the following pairs of bonded

elements forms the more polar bond?

95 A(n) chemical bond represents the equal

sharing of a pair of electrons between two nuclei.

96 For each of the following pairs of elements, identify

which element would be expected to be more

elec-tronegative It should not be necessary to look at a

table of actual electronegativity values.

a Be or Ba

b N or P

c F or Cl

bonds would be expected to be ionic, covalent, or

a NOP or NOO c NOS or NOC

b NOC or NOO d NOF or NOS

100 In each of the following molecules, which end of the

molecule is negative relative to the other end?

a carbon monoxide, CO

b iodine monobromide, IBr

c hydrogen iodide, HI

indicat-ing the direction of the bond dipole, includindicat-ing which

end of the bond is positive and which is negative.

a NOCl c NOS

b NOP d NOC

102 Write the electron configuration for each of the

fol-lowing atoms and for the simple ion that the element

most commonly forms In each case, indicate which

noble gas has the same electron configuration as the

103 What simple ion does each of the following elements

most commonly form?

a sodium e sulfur

b iodine f magnesium

c potassium g aluminum

d calcium h nitrogen

the formula of the simple binary ionic compound likely to form when the following pairs of elements react with each other.

a sodium, Na, and selenium, Se

b rubidium, Rb, and fluorine, F

c potassium, K, and tellurium, Te

d barium, Ba, and selenium, Se

e potassium, K, and astatine, At

f francium, Fr, and chlorine, Cl

105 Which noble gas has the same electron configuration

as each of the ions in the following compounds?

a calcium bromide, CaBr2

108 What is the total number of valence electrons in each

of the following molecules?

a HNO3 c H3PO4

b H2SO4 d HClO4

simple molecules Show all bonding valence tron pairs as lines and all nonbonding valence electron pairs as dots.

elec-a GeH4 c NI3

b Icl d PF3

simple molecules Show all bonding valence tron pairs as lines and all nonbonding valence electron pairs as dots.

elec-a N2H4 c NCl3

b C2H6 d SiCl4

simple molecules Show all bonding valence tron pairs as lines and all nonbonding valence electron pairs as dots For those molecules that exhibit

elec-Chapter Review 397

Trang 29

resonance, draw the various possible resonance

forms.

a SO2

b N2O (N in center)

c O3

as lines and all nonbonding valence electron pairs as

dots For those ions that exhibit resonance, draw the

various possible resonance forms.

a nitrate ion

b carbonate ion

c ammonium ion

113 Why is the molecular structure of H2O nonlinear,

whereas that of BeF2is linear, even though both

mol-ecules consist of three atoms?

mol-ecules, give the number and the arrangement of the

electron pairs around that atom.

a C in CCl4

b Ge in GeH4

c B in BF3

a Cl2O

b OF2

c SiCl4

a chlorate ion

b chlorite ion

c perchlorate ion

117 For each of the following molecules, indicate the

bond angle expected between the central atom and any two adjacent chlorine atoms.

a Cl2O c BeCl2

b CCl4 d BCl3

struc-ture of each of the following molecules or ions taining multiple bonds.

con-a SO2

b SO3

c HCO3(hydrogen is bonded to oxygen)

d HCN

struc-ture of each of the following molecules or ions taining multiple bonds.

con-a CO3

b HNO3(hydrogen is bonded to oxygen)

c NO2

d C2H2

120 Explain briefly how substances with ionic bonding

differ in properties from substances with covalent bonding.

121 Explain the difference between a covalent bond

formed between two atoms of the same element and

a covalent bond formed between atoms of two ent elements.

differ-398 Chapter 12 Chemical Bonding

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are used for What does it mean to “crack” petroleum and why is this done? What was tetraethyl lead used for, and why has its use been drastically reduced?

What is the greenhouse effect, and why are scientists

concerned about it?

10 What is a driving force? Name two common and

im-portant driving forces, and give an example of each.

What is entropy? Although the total energy of the verse is constant, is the entropy of the universe con-

uni-stant? What is a spontaneous process?

11 Suppose we have separate 25-g samples of iron, silver,

and gold If 125 J of heat energy is applied separately

to each of the three samples, show by calculation which sample will end up at the highest temperature.

12 Methane, CH4, is the major component of natural gas Methane burns in air, releasing approximately

890 kJ of heat energy per mole.

meth-c What quantity of methane must have reacted if

1250 kJ of heat energy was released?

13 What is electromagnetic radiation? Give some

exam-ples of such radiation Explain what the wavelength

(␭) and frequency (␯) of electromagnetic radiation

rep-resent Sketch a representation of a wave and indicate

on your drawing one wavelength of the wave At what speed does electromagnetic radiation move through space? How is this speed related to ␭ and ␯?

14 Explain what it means for an atom to be in an excited

state and what it means for an atom to be in its ground state How does an excited atom return to its ground state? What is a photon? How is the wavelength

(color) of light related to the energy of the photons being emitted by an atom? How is the energy of the

photons being emitted by an atom related to the ergy changes taking place within the atom?

en-15 Do atoms in excited states emit radiation randomly,

at any wavelength? Why? What does it mean to say

that the hydrogen atom has only certain discrete ergy levels available? How do we know this? Why was

en-the quantization of energy levels surprising to tists when it was first discovered?

scien-16 Describe Bohr’s model of the hydrogen atom How

did Bohr envision the relationship between the tron and the nucleus of the hydrogen atom? How did Bohr’s model explain the emission of only discrete wavelengths of light by excited hydrogen atoms? Why did Bohr’s model not stand up as more experiments were performed using elements other than hydrogen?

elec-C U M U L A T I V E R E V I E W f o r elec-C H A P T E R S 10-12

QUESTIONS

1 What is potential energy? What is kinetic energy?

What do we mean by the law of conservation of energy?

What do scientists mean by work? Explain what

sci-entists mean by a state function and give an example

of one.

2 What does temperature measure? Are the molecules in

a beaker of warm water moving at the same speed as

the molecules in a beaker of cold water? Explain.

What is heat? Is heat the same as temperature?

3 When describing a reaction, a chemist might refer to

the system and the surroundings Explain each of these

terms If a reaction is endothermic, does heat travel

from the surroundings into the system, or from the

system into the surroundings? Suppose a reaction

be-tween ionic solutes is performed in aqueous solution,

and the temperature of the solution increases Is the

reaction exothermic or endothermic? Explain.

4 What is the study of energy and energy changes

called? What is the “first law” of thermodynamics

and what does it mean? What do scientists mean by

the internal energy of a system? Is the internal energy

the same as heat?

5 How is the calorie defined? Is the thermodynamic

calo-rie the same as the Calocalo-rie we are careful of when

planning our diets? Although the calorie is our

“working unit” of energy (based on its experimental

definition), the SI unit of energy is the joule How are

joules and calories related? What does the specific heat

capacity of a substance represent? What common

sub-stance has a relatively high specific heat capacity,

which makes it useful for cooling purposes?

6 What is the enthalpy change for a process? Is enthalpy

a state function? In what experimental apparatus are

enthalpy changes measured?

7 Hess’s law is often confusing to students Imagine

you are talking to a friend who has not taken any

sci-ence courses Using the reactions

P4(s) 6Cl 2( g) S 4PCl3( g) H 2.44 103 kJ

4PCl5( g) S P4(s) 10Cl 2( g) H 3.43 103 kJ

Explain to your friend how Hess’s law can be used to

calculate the enthalpy change for the reaction

PCl5( g) S PCl3( g) Cl 2( g)

8 The first law of thermodynamics indicates that the

total energy content of the universe is constant If

this is true, why do we worry about “energy

conser-vation”? What do we mean by the quality of energy,

rather than the quantity? Give an example Although

the quantity of energy in the universe may be

con-stant, is the quality of that energy changing?

9 What do petroleum and natural gas consist of? Indicate

some petroleum “fractions” and explain what they

Trang 31

17 Schrödinger and de Broglie suggested a

“wave–parti-cle duality” for small parti“wave–parti-cles—that is, if

electromag-netic radiation showed some particle-like properties,

then perhaps small particles might exhibit some

wave-like properties Explain How does the wave

mechanical picture of the atom fundamentally differ

from the Bohr model? How do wave mechanical

or-bitals differ from Bohr’s orbits? What does it mean to

say that an orbital represents a probability map for an

electron?

18 Describe the general characteristics of the first

(low-est-energy) hydrogen atomic orbital How is this

or-bital designated symbolically? Does this oror-bital have

a sharp “edge”? Does the orbital represent a surface

upon which the electron travels at all times?

19 Use the wave mechanical picture of the hydrogen

atom to describe what happens when the atom

absorbs energy and moves to an “excited” state.

What do the principal energy levels and their sublevels

represent for a hydrogen atom? How do we designate

specific principal energy levels and sublevels in

hydrogen?

20 Describe the sublevels and orbitals that constitute the

third and fourth principal energy levels of hydrogen.

How is each of the orbitals designated and what are

the general shapes of their probability maps?

21 Describe electron spin How does electron spin affect

the total number of electrons that can be

accommo-dated in a given orbital? What does the Pauli exclusion

principle tell us about electrons and their spins?

22 Summarize the postulates of the wave mechanical

model of the atom.

23 List the order in which the orbitals are filled as the

atoms beyond hydrogen are built up How many

electrons overall can be accommodated in the first

and second principal energy levels? How many

elec-trons can be placed in a given s subshell? In a given p

subshell? In a specific p orbital? Why do we assign

unpaired electrons in the 2p orbitals of carbon,

nitro-gen, and oxygen?

24 Which are the valence electrons in an atom? Choose

three elements and write their electron

tions, circling the valence electrons in the

configura-tions Why are the valence electrons more important

to an atom’s chemical properties than are the core

electrons or the nucleus?

25 Sketch the overall shape of the periodic table and

in-dicate the general regions of the table that represent

the various s, p, d, and f orbitals being filled How is

an element’s position in the periodic table related to

its chemical properties?

26 Using the general periodic table you developed in

Question 25, show how the valence-electron

config-uration of most of the elements can be written just by

knowing the relative location of the element on the

table Give specific examples.

27 What are the representative elements? In what region(s)

of the periodic table are these elements found? In

what general area of the periodic table are the lic elements found? In what general area of the table are the nonmetals found? Where in the table are the metalloids located?

metal-28 You have learned how the properties of the

ele-ments vary systematically, corresponding to the

elec-tron structures of the elements being considered.

Discuss how the ionization energies and atomic sizes

of elements vary, both within a vertical group ily) of the periodic table and within a horizontal row (period).

(fam-29 In general, what do we mean by a chemical bond?

What does the bond energy tell us about the strength

of a chemical bond? Name the principal types of chemical bonds.

30 What do we mean by ionic bonding? Give an

exam-ple of a substance whose particles are held together

by ionic bonding What experimental evidence do

we have for the existence of ionic bonding? In eral, what types of substances react to produce compounds having ionic bonding?

gen-31 What do we mean by covalent bonding and polar

co-valent bonding? How are these two bonding types

similar and how do they differ? What circumstance must exist for a bond to be purely covalent? How does a polar covalent bond differ from an ionic bond?

32 What is meant by electronegativity? How is the

differ-ence in electronegativity between two bonded atoms related to the polarity of the bond? Using Figure 12.3, give an example of a bond that would be nonpolar and of a bond that would be highly polar.

33 What does it mean to say that a molecule has a dipole

moment? What is the difference between a polar bond

and a polar molecule (one that has a dipole ment)? Give an example of a molecule that has polar bonds and that has a dipole moment Give an example of a molecule that has polar bonds, but that does

mo-not have a dipole moment What are some

implica-tions of the fact that water has a dipole moment?

34 How is the attainment of a noble gas electron

config-uration important to our ideas of how atoms bond to each other? When atoms of a metal react with atoms

of a nonmetal, what type of electron configurations

do the resulting ions attain? Explain how the atoms

in a covalently bonded compound can attain noble gas electron configurations.

35 Give evidence that ionic bonds are very strong Does

an ionic substance contain discrete molecules? With what general type of structure do ionic compounds occur? Sketch a representation of a general structure for an ionic compound Why is a cation always smaller and an anion always larger than the respec- tive parent atom? Describe the bonding in an ionic compound containing polyatomic ions.

400

400 Cumulative Review for Chapters 10–12

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36 Why does a Lewis structure for a molecule show only

the valence electrons? What is the most important

fac-tor for the formation of a stable compound? How do

we use this requirement when writing Lewis structures?

37 In writing Lewis structures for molecules, what is

meant by the duet rule? To which element does the

duet rule apply? What do we mean by the octet rule?

Why is attaining an octet of electrons important for

an atom when it forms bonds to other atoms? What

is a bonding pair of electrons? What is a nonbonding

(or lone) pair of electrons?

38 For three simple molecules of your own choice, apply

the rules for writing Lewis structures Write your

dis-cussion as if you are explaining the method to

some-one who is not familiar with Lewis structures.

39 What does a double bond between two atoms

repre-sent in terms of the number of electrons shared?

What does a triple bond represent? When writing a

Lewis structure, explain how we recognize when a

molecule must contain double or triple bonds What

are resonance structures?

40 Although many simple molecules fulfill the octet

rule, some common molecules are exceptions to this

rule Give three examples of molecules whose Lewis

structures are exceptions to the octet rule.

41 What do we mean by the geometric structure of a

mol-ecule? Draw the geometric structures of at least four

simple molecules of your choosing and indicate the

bond angles in the structures Explain the main ideas

of the valence shell electron pair repulsion (VSEPR)

the-ory Using several examples, explain how you would

apply the VSEPR theory to predict their geometric

structures.

42 What bond angle results when there are only two

va-lence electron pairs around an atom? What bond gle results when there are three valence pairs? What bond angle results when there are four pairs of valence electrons around the central atom in a molecule? Give examples of molecules containing these bond angles.

an-43 How do we predict the geometric structure of a

mol-ecule whose Lewis structure indicates that the cule contains a double or triple bond? Give an example of such a molecule, write its Lewis structure, and show how the geometric shape is derived.

mole-44 Write the electron configuration for the following

atoms, using the appropriate noble gas to abbreviate the configuration of the core electrons.

a Sr, Z 38 d K, Z 19

b Al, Z 13 e S, Z 16

c Cl, Z 17 f As, Z 33

45 Based on the electron configuration of the simple

ions that the pairs of elements given below would be expected to form, predict the formula of the simple binary compound that would be formed by each pair.

a Al and F d Mg and P

b Li and N e Al and O

c Ca and S f K and S

46 Draw the Lewis structure for each of the following

molecules or ions Indicate the number and spatial orientation of the electron pairs around the boldface atom in each formula Predict the simple geometric structure of each molecule or ion, and indicate the approximate bond angles around the boldface atom.

Trang 33

A cluster balloonist at an Iowa fair Clusterballoonists use a large number of relatively

small helium balloons (AP Photo/The Daily Nonpareil/Ben DeVries)

1 3 5 The Ideal Gas Law

1 3 6 Dalton’s Law of Partial

1 3 9 The Implications of the

Kinetic Molecular Theory

1 3 1 0 Gas Stoichiometry

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We live immersed in a gaseous solution The earth’s atmosphere is amixture of gases that consists mainly of elemental nitrogen, N2, and oxy-gen, O2 The atmosphere both supports life and acts as a waste receptaclefor the exhaust gases that accompany many industrial processes Thechemical reactions of these waste gases in the atmosphere lead to varioustypes of pollution, including smog and acid rain The two main sources ofpollution are transportation and the production of electricity The com-bustion of fuel in vehicles produces CO, CO2, NO, and NO2, along withunburned fragments of the petroleum used as fuel The combus-tion of coal and petroleum in power plants produces NO2and SO2in the exhaust gases These mixtures of chemicalscan be activated by absorbing light to produce the pho-tochemical smog that afflicts most large cities The SO2

in the air reacts with oxygen to produce SO3 gas,which combines with water in the air to producedroplets of sulfuric acid (H2SO4), a major compo-nent of acid rain

The gases in the atmosphere also shield usfrom harmful radiation from the sun and keep theearth warm by reflecting heat radiation back to-ward the earth In fact, there is now great concernthat an increase in atmospheric carbon dioxide, aproduct of the combustion of fossil fuels, is causing

a dangerous warming of the earth (See “Chemistry

in Focus: Atmospheric Effects,” in Chapter 11.)

In this chapter we will look carefully at the erties of gases First, we will see how measurements of gasproperties lead to various types of laws—statements thatshow how the properties are related to each other Then we willconstruct a model to explain why gases behave as they do This modelwill show how the behavior of the individual particles of a gas leads to theobserved properties of the gas itself (a collection of many, many particles).The study of gases provides an excellent example of the scientificmethod in action It illustrates how observations lead to natural laws,which in turn can be accounted for by models

com-13.1 Pressure 403

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Steve Fossett flies his balloon

Solo Spirit, over the east coast of

Australia during his attempt to

make the first solo balloon flight

around the world.

O B J E C T I V E S :

13.1

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The gases most familiar to us form the earth’s atmosphere The pressureexerted by this gaseous mixture that we call air can be dramatically demon-strated by the experiment shown in Figure 13.1 A small volume of water isplaced in a metal can and the water is boiled, which fills the can with steam.The can is then sealed and allowed to cool Why does the can collapse as itcools? It is the atmospheric pressure that crumples the can When the can iscooled after being sealed so that no air can flow in, the water vapor (steam)inside the can condenses to a very small volume of liquid water As a gas, thewater vapor filled the can, but when it is condensed to a liquid, the liquiddoes not come close to filling the can The H2O molecules formerly present

as a gas are now collected in a much smaller volume of liquid, and there arevery few molecules of gas left to exert pressure outward and counteract theair pressure As a result, the pressure exerted by the gas molecules in the at-mosphere smashes the can

A device that measures atmospheric pressure, the barometer, was

in-vented in 1643 by an Italian scientist named Evangelista Torricelli (1608–1647), who had been a student of the famous astronomer Galileo Torricelli’sbarometer is constructed by filling a glass tube with liquid mercury and in-verting it in a dish of mercury, as shown in Figure 13.2 Notice that a largequantity of mercury stays in the tube In fact, at sea level the height of thiscolumn of mercury averages 760 mm Why does this mercury stay in thetube, seemingly in defiance of gravity? Figure 13.2 illustrates how the pres-sure exerted by the atmospheric gases on the surface of mercury in the dishkeeps the mercury in the tube

404 Chapter 13 Gases

Dry air (air from which the

water vapor has been removed)

is 78.1% N2molecules, 20.9%

O2molecules, 0.9% Ar atoms,

and 0.03% CO2molecules,

along with smaller amounts of

Ne, He, CH4, Kr, and other trace

components

As a gas, water occupies 1200

times as much space as it does

as a liquid at 25 °C and

atmospheric pressure

Soon after Torricelli died, a

German physicist named Otto

von Guericke invented an air

pump In a famous

demonstra-tion for the King of Prussia in

1683, Guericke placed two

hemi-spheres together, pumped the air

out of the resulting sphere

through a valve, and showed

that teams of horses could not

pull the hemispheres apart Then,

after secretly opening the air

valve, Guericke easily separated

the hemispheres by hand The

King of Prussia was so impressed

that he awarded Guericke a

life-time pension!

a

The pressure exerted by the gases in the atmosphere can be demonstrated by boiling water in a can and then turning off the heat and sealing the can.

b

As the can cools, the water vapor condenses, lowering the gas pressure inside the can This causes the can to crumple.

Figure 13.1

Empty space (a vacuum)

Hg

Weight of the mercury in the column

Weight of the atmosphere (atmospheric pressure)

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Atmospheric pressure results from the mass of the air being pulled ward the center of the earth by gravity—in other words, it results from theweight of the air Changing weather conditions cause the atmospheric pres-sure to vary, so the height of the column of Hg supported by the atmosphere

to-at sea level varies; it is not always 760 mm The meteorologist who says a

“low” is approaching means that the atmospheric pressure is going to crease This condition often occurs in conjunction with a storm

de-Atmospheric pressure also varies with altitude For example, when ricelli’s experiment is done in Breckenridge, Colorado (elevation 9600 feet),the atmosphere supports a column of mercury only about 520 mm high be-cause the air is “thinner.” That is, there is less air pushing down on theearth’s surface at Breckenridge than at sea level

Tor-Units of Pressure

Because instruments used for measuring pressure (see Figure 13.3) often tain mercury, the most commonly used units for pressure are based on theheight of the mercury column (in millimeters) that the gas pressure can sup-

con-port The unit mm Hg (millimeters of mercury) is often called the torr in

honor of Torricelli The terms torr and mm Hg are used interchangeably by

chemists A related unit for pressure is the standard atmosphere

(abbre-viated atm)

The SI unit for pressure is the pascal (abbreviated Pa).

Thus 1 atmosphere is about 100,000 or 105pascals Because the pascal is sosmall we will use it sparingly in this book A unit of pressure that is employed

1 standard atmosphere 101,325 Pa

1 standard atmosphere 1.000 atm 760.0 mm Hg 760.0 torr

13.1 Pressure 405

Mercury is used to measure

pressure because of its high

density By way of comparison,

the column of water required

to measure a given pressure

would be 13.6 times as high

as a mercury column used

for the same purpose

Gas pressure = atmospheric pressure – h.

Gas pressure = atmospheric pressure + h.

Atmospheric pressure

Gas pressure less than atmospheric pressure

Hg

Gas pressure greater than atmospheric pressure

Atmospheric pressure

Figure 13.3

A device (called a manometer)

for measuring the pressure

of a gas in a container The

pressure of the gas is equal

to h (the difference in mercury

levels) in units of torr

(equivalent to mm Hg).

Trang 37

in the engineering sciences and that we use for measuring tire pressure ispounds per square inch, abbreviated psi.

Sometimes we need to convert from one unit of pressure to another We

do this by using conversion factors The process is illustrated in Example 13.1

Pressure Unit Conversions

The pressure of the air in a tire is measured to be 28 psi Represent this sure in atmospheres, torr, and pascals

pres-S O L U T I O N

Where Are We Going?

We want to convert from units of pounds per square inch to units of pheres, torr, and pascals

atmos-What Do We Know?

• 28 psi

What Information Do We Need?

• We need the equivalence statements for the units

How Do We Get There?

To convert from pounds per square inch to atmospheres, we need the alence statement

equiv-which leads to the conversion factor

To convert from atmospheres to torr, we use the equivalence statement

which leads to the conversion factor

To change from torr to pascals, we need the equivalence statement

which leads to the conversion factor

R E A L I T Y C H E C K The units on the answers are the units required

1.9 atm 101,325 Pa

1.000 atm 1.9 105 Pa

101,325 Pa1.000 atm1.000 atm 101,325 Pa

1.9 atm 760.0 torr

1.000 atm 1.4 103 torr

760.0 torr1.000 atm1.000 atm 760.0 torr

28 psi 1.000 atm

14.69 psi 1.9 atm

1.000 atm14.69 psi1.000 atm 14.69 psi

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On a summer day in Breckenridge, Colorado, the atmospheric pressure is

525 mm Hg What is this air pressure in atmospheres?

See Problems 13.7 through 13.12 ■

Pressure and Volume: Boyle’s Law

To understand the law that relates the pressure and volume of a gas • To

do calculations involving this law.

The first careful experiments on gases were performed by the Irish scientistRobert Boyle (1627–1691) Using a J-shaped tube closed at one end (Fig-ure 13.4), which he reportedly set up in the multi-story entryway of hishouse, Boyle studied the relationship between the pressure of the trappedgas and its volume Representative values from Boyle’s experiments are given

in Table 13.1 The units given for the volume (cubic inches) and pressure(inches of mercury) are the ones Boyle used Keep in mind that the metricsystem was not in use at this time

First let’s examine Boyle’s observations (Table 13.1) for general trends.Note that as the pressure increases, the volume of the trapped gas decreases

In fact, if you compare the data from experiments 1 and 4, you can see that

as the pressure is doubled (from 29.1 to 58.2), the volume of the gas is halved(from 48.0 to 24.0) The same relationship can be seen in experiments 2 and

5 and in experiments 3 and 6 (approximately)

We can see the relationship between the volume of a gas and its sure more clearly by looking at the product of the values of these two prop-

pres-erties (P V) using Boyle’s observations This product is shown in the last

column of Table 13.1 Note that for all the experiments,

with only a slight variation due to experimental error Other similar surements on gases show the same behavior This means that the relation-ship of the pressure and volume of a gas can be expressed in words as

mea-pressure times volume equals a constant

Figure 13.4

A J-tube similar to the one used

by Boyle The pressure on the

trapped gas can be changed by

adding or withdrawing mercury.

For Boyle’s law to hold, the

amount of gas (moles) must not

be changed The temperature

must also be constant

The fact that the constant is

sometimes 1.40 103instead

of 1.41 103is due to

experimental error (uncertainties

in measuring the values of P

Trang 39

or in terms of an equation as

which is called Boyle’s law, where k is a constant at a specific temperature

for a given amount of gas For the data we used from Boyle’s experiment, k1.41 103(in Hg) in.3

It is often easier to visualize the relationships between two properties if

we make a graph Figure 13.5 uses the data given in Table 13.1 to show howpressure is related to volume This relationship, called a plot or a graph,

shows that V decreases as P increases When this type of relationship exists,

we say that volume and pressure are inversely related or inversely proportional;

when one increases, the other decreases Boyle’s law is illustrated by the gassamples in Figure 13.6

Boyle’s law means that if we know the volume of a gas at a given

pres-sure, we can predict the new volume if the pressure is changed, provided that neither the temperature nor the amount of gas is changed For example, if we represent the original pressure and volume as P1and V1and the final values as

P2and V2, using Boyle’s law we can write

and

We can also say

or simply

This is really another way to write Boyle’s law We can solve for the final

vol-ume (V2) by dividing both sides of the equation by P2

Canceling the P2terms on the right gives

Illustration of Boyle’s law These

three containers contain the

same number of molecules At

298 K, P V 1 L atm in all

three containers.

Trang 40

This equation tells us that we can calculate the new gas volume (V2) by

mul-tiplying the original volume (V1) by the ratio of the original pressure to the

final pressure (P1/P2), as illustrated in Example 13.2

Calculating Volume Using Boyle’s Law

Freon-12 (the common name for the compound CCl2F2) was widely used inrefrigeration systems, but has now been replaced by other compounds that

do not lead to the breakdown of the protective ozone in the upper phere Consider a 1.5-L sample of gaseous CCl2F2at a pressure of 56 torr Ifpressure is changed to 150 torr at a constant temperature,

atmos-a Will the volume of the gas increase or decrease?

b What will be the new volume of the gas?

S O L U T I O N

Where Are We Going?

We want to determine if the volume will increase or decrease when the sure is changed, and we want to calculate the new volume

pres-What Do We Know?

• We know the initial and final pressures and the initial volume

• The amount of gas and temperature are held constant

• Boyle’s law: P1V1 P2V2

How Do We Get There?

a As the first step in a gas law problem, always write down theinformation given, in the form of a table showing the initial andfinal conditions

Initial Conditions Final Conditions

EXAMPLE 13.2

P2V2

P1V1

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